Row Echelon Form Calculator

About this calculator

Row echelon form (REF) is what you get after applying Gaussian elimination to a matrix: using row operations to zero out everything below each pivot, creating a staircase pattern of leading entries. It's the standard first step in solving systems of linear equations by hand or by computer.

This calculator reduces a 3×3 matrix using forward elimination with partial pivoting (swapping rows to put the largest available value on the pivot for numerical stability), and reports the matrix's rank (number of non-zero pivot rows) and determinant along the way — core operations in linear algebra courses and in engineering fields that solve systems of equations, from circuit analysis to structural mechanics.